The measurement of electrical impedance in the high-frequency range (loosely speaking, from 100 kHz to 100 MHz) is a common characterization technique in research and applications concerning condensed matter physics, engineering and biology. Commercial instruments for impedance measurement have specifications, including frequency range and base accuracy, continuously improving. The calibration of impedance instruments and standards in the high-frequency range represents a tough challenge for metrology laboratories; measurement methods and traceability paths are not as firmly established as those employed for lower (audio) or higher (microwave) frequencies. In the last few years, the problem has received increased attention from the metrology community. The paper gives a review of recent results in the field.

http://iopscience.iop.org/article/10.1088/0957-0233/20/2/022002/pdf

The metrology of electrical impedance at high frequency: a review

https://iopscience.iop.org/article/10.1088/1681-7575/aacf6c/pdf

Impedance bridges: from Wheatstone to Josephson

Techniques related to the establishment and the comparison of primary standards of resistance and capacitance are described and discussed. In the field of resistance, the characteristics of primary standard resistors of 1 Ω and 10 000 Ω are presented and dc resistance-ratio measurement techniques reviewed, including the series-parallel method, the Warshawsky bridge and the cryogenic current comparator bridge. A review of techniques and results regarding very low-frequency ac measurements of dc standard resistors is also given. In the field of capacitance, the realization of the farad using calculable standards is discussed as well as the techniques for accurate measurements of four terminal-pair impedances used in particular for linking the farad and the ohm.

https://iopscience.iop.org/article/10.1088/0026-1394/29/2/001/pdf

DC and AC Techniques for Resistance and Impedance Measurements

A bridge to calibrate programmable and manual inductive voltage dividers is described. The bridge is based on a programmable 30-b binary inductive voltage divider with terminal linearity of +or-0.1 ppm in phase and +or-2 ppm quadrature at 400 Hz. Measurements of programmable test dividers can be automated using software developed to align the bridge components and perform an automatic balance. >

Automatic inductive voltage divider bridge for operation from 10 Hz to 100 kHz

This paper describes a simple, passive, low-cost resistance network, closely related to Hamon build-up resistors, that enables the calibration of dc and low-frequency ac resistance and conductance bridges. The network is configured so that the four component resistors can be connected to realize 35 distinct four-terminal resistances, all interrelated by the usual formulas for the series and parallel connections of resistors. Theoretical analysis and experimental results show that with due care in the design, the network can be readily constructed to achieve an accuracy of better than 1 /spl mu//spl Omega/ for resistances of the order of 100 /spl Omega/ (1:10/sup 8/) for angular frequencies from dc to 10/sup 4/ rad/s.

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A simple resistance network for calibrating resistance bridges

The paper examines the theory of the 2-stage voltage transformer and shows that it not only provides a very accurate primary/secondary voltage ratio but also increases the effective input impedance of one of its primary windings to a very high value. It is shown theoretically and experimentally that these characteristics enable inductive voltage dividers to be made which have extremely small errors of voltage division within individual decades and in which the errors due to interconnecting the decades are virtually eliminated. Single-decade dividers having in-phase errors of less than 5 parts in 109 of the input over the frequency band 40–400 Hz have been constructed.

Two-stage inductive voltage dividers

The causes of error in inductive voltage dividers are examined in detail, and equations are developed from which the voltage ratios may be predicted with an uncertainty not exceeding 1 part in 108. Experimental methods for measurement of the voltage ratios to an accuracy of within 2 parts in 109 of the input-voltage vector are fully described, together with techniques by which the constituent parts of the overall error may be isolated. The paper also describes an improved method of winding decade inductive dividers and gives specifications for multidecade devices in which the errors predictably will not exceed 1 part in 108 at 400Hz or 5 parts in 108 over the whole frequency range 40-1592 Hz.

Theory, design and measurement of inductive voltage dividers

The causes of error in inductive voltage dividers are examined in detail, and equations are developed from which the voltage ratios may be predicted with an uncertainty not exceeding 1 part in 108. Experimental methods for measurement of the voltage ratios to an accuracy of 2 parts in 109 of the input voltage vector are fully described, together with techniques by which the constituent parts of the overall error may be isolated. An improved method of winding decade inductive dividers is also described and specifications are given for multidecade devices in which the errors predictably will not exceed 1 part in 108 at 400 Hz or 5 parts in 108 over the whole frequency range 40 to 1592 Hz.

Voltage-Ratio Measurement with a Precision of Parts in 109 and Performance of Inductive Voltage Dividers

https://ieeexplore.ieee.org/iel5/19/4313707/04313718.pdf

J.J. Hill

Papers

Two-stage inductive voltage dividers

Theory, design and measurement of inductive voltage dividers

Voltage-Ratio Measurement with a Precision of Parts in 109 and Performance of Inductive Voltage Dividers

Voltage-Ratio Measurement witha PrecisionofParts